(x-7)(x+3)=39

Solution for (x-7)(x+3)=39 equation:

Simplifying
(x + -7)(x + 3) = 39

Reorder the terms:
(-7 + x)(x + 3) = 39

Reorder the terms:
(-7 + x)(3 + x) = 39

Multiply (-7 + x) * (3 + x)
(-7(3 + x) + x(3 + x)) = 39
((3 * -7 + x * -7) + x(3 + x)) = 39
((-21 + -7x) + x(3 + x)) = 39
(-21 + -7x + (3 * x + x * x)) = 39
(-21 + -7x + (3x + x2)) = 39

Combine like terms: -7x + 3x = -4x
(-21 + -4x + x2) = 39

Solving
-21 + -4x + x2 = 39

Solving for variable 'x'.

Reorder the terms:
-21 + -39 + -4x + x2 = 39 + -39

Combine like terms: -21 + -39 = -60
-60 + -4x + x2 = 39 + -39

Combine like terms: 39 + -39 = 0
-60 + -4x + x2 = 0

Factor a trinomial.
(-6 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-6, 10}